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a) \(2x-2y-x^2+2xy-y^2\)
\(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(2-x+y\right)\)
b) \(9x^2+6xy+y^2-25\)
\(=\left(3x\right)^2+6xy+y^2-25\)
\(=\left(3x+y\right)^2-5^2\)
\(=\left(3x+y+5\right)\left(3x+y-5\right)\)
\(a,x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right).\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right).\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(b,9x^2+y^2+6xy=\left(3x\right)^2+2.3x.y+y^2=\left(3x+y\right)^2\)
\(c,6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x^2-2.x.3+3^2\right)=-\left(x-3\right)^2\)
a) \(3x^2-6xy+3y^2-12z^2\)
\(=3\left(x^2-2xy+y^2-4z^2\right)\)
\(=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)
b) \(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y+5\right)\left(x+y-5\right)\)
\(25-9x^2-6xy-y^2\)
\(=25-\left(9x^2+6xy+y^2\right)\)
\(=5^2-\left(3x+y\right)^2\)
\(=\left(5-3x-y\right)\left(5+3x+y\right)\)